a: \(\text{Δ}=\left(-2m\right)^2-4\left(m-3\right)\)
=4m^2-4m+12
=(2m-1)^2+11>0
=>PT luôn có hai nghiệm pb
b: \(P=4\left(x_1\cdot x_2\right)^2+2\left(x_1^2+x_2^2\right)+1\)
\(=4\cdot\left(m-3\right)^2+2\left[\left(-2m\right)^2-2\left(m-3\right)\right]+1\)
\(=4\left(m^2-6m+9\right)+2\left(4m^2-2m+6\right)+1\)
\(=4m^2-24m+36+8m^2-4m+12+1\)
\(=12m^2-28m+49\)
\(=12\left(m^2-\dfrac{7}{3}m+\dfrac{49}{12}\right)\)
\(=12\left(m^2-2\cdot m\cdot\dfrac{7}{6}+\dfrac{49}{36}+\dfrac{49}{18}\right)\)
\(=12\left(m-\dfrac{7}{6}\right)^2+\dfrac{147}{2}>=\dfrac{147}{2}\)
Dấu = xảy ra khi m=7/6
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